DIFFERENTIAL EQUATION (MT-202) SYED AZEEM INAM

DIFFERENTIAL EQUATION (MT-202)

LECTURE #9

SOME APPLICATIONS OF SEPARABLE DIFFERENTIAL EQUATIONS:

EXAMPLE#1: THE MATHEMATICAL POLICEWOMAN

A murder victim is discovered, and lieutenant from the forensic science laboratory

is summoned to estimate the time of death. The body is located in a room that is kept

at a constant 68 0F. For some time after death, the body will radiate heat into the

cooler room, causing the body’s temperature decrease. Assuming(for want better

information) that the victims temperature was a normal 98.6 0F at time of death the

lieutenant will try to estimate this time by observing’s the body’s current temperature

and calculating how long it would have had to lose heat to reach this point. The

lieutenant arrived at 9:40 p.m. where temperature was 94.4 0F whereas at 11:00 p.m.

temperature was 89.2 0F

EXAMPLE #2: RADIOACTIVE DECAY AND CARBON DATING

In radioactive decay, mass is converted to energy by radiation. It has been observed

that the rate of change of the mass of a radioactive substance is proportional to the

mass itself.